Timeline for Using Quotient of Prime Numbers to Approximation Reals
Current License: CC BY-SA 3.0
4 events
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| Dec 20, 2020 at 1:05 | comment | added | Timothy Chow | @KConrad : Yes, I remember asking that question back then, but I no longer recall if I came up with the question myself or heard it from someone else first. | |
| Dec 20, 2020 at 0:43 | comment | added | KConrad | Tim, you posed Question 1 yourself in 1990 during that course we took using Serre's Course in Arithmetic. I was presenting material from the section on Dirichlet's theorem, and with that on my mind I noticed that if Dirichlet's theorem admits a stronger form where $\gcd(a,b) = 1 \Rightarrow an+b$ and $bn+a$ are both prime (together) for infinitely many $n$ then from $(an+b)/(bn+a) \to a/b$ as $n \to \infty$ we'd get the ratios of primes to be dense in $\mathbf Q_{>0}$ and thus also dense in $\mathbf R_{>0}$. The next year I found the right context for that in the Bateman-Horn conjecture. | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Dec 26, 2012 at 0:54 | history | answered | Timothy Chow | CC BY-SA 3.0 |